The Study Of P-expandable Spaces And P-paracompact Spaces

In this thesis, p-exp-andable sp-aces, p-countably exp-andable sp-aces,p-p-aracomp-act sp-aces, p-countably p-aracomp-act sp-aces, three kindsof locally p-p-aracomp-act sp-aces in general top-ological sp-aces, p-Ip-aracomp-act sp-aces and p-Ⅱ p-aracomp-act sp-aces in L-top-ological aredefined and investigated. The p-rimary contents are as follows:Firstly, to introduce the concep-ts of p-exp-andable sp-aces andp-countably exp-andable sp-aces with p-reop-en sets. The equivalence ofthem under some conditions is showed. The connections betweenp-exp-andable sp-aces and some other exp-andable sp-aces arediscussed.Secondly, by using p-reop-en sets and covering p-rop-erty theory,we obtain the definitions and the equivalence conditions ofp-p-aracomp-act sp-aces and p-countably p-aracomp-act sp-aces, andgives the p-rop-erties of p-p-aracomp-act subset.Thirdly, to introduce the concep-ts of the three kinds of locallyp-p-aracomp-act sp-aces with p-reop-en sets and investigate the heritabilityp-rop-erties,map-p-ing p-rop-erties, p-roduct p-rop-erties,top-ological sump-rop-erties and sep-aration p-rop-erties.At last, the concep-t of p-p-aracomp-act sp-aces in general top-ologicalsp-aces is extended to L-top-ological sp-aces and the concep-ts of p-Ip-aracomp-act sp-aces and p-Ⅱ p-aracomp-act sp-aces are obtained. Thep-rop-erties of them are studied. It is p-roved that p-I p-aracomp-act andp-Ⅱ p-aracomp-act are “good extension” and “L-good extension”resp-ectively.